Answer :
Answer:
[tex]NK = 15[/tex]
[tex]JL = 26[/tex]
[tex]KL = 19.85[/tex]
[tex]\angle JKM =49[/tex]
[tex]\angle JML =41[/tex]
[tex]\angle MLK = 90[/tex]
[tex]\angle MNL =90[/tex]
[tex]\angle KJL =41[/tex]
Step-by-step explanation:
Given
[tex]MK = 30[/tex]
[tex]NL = 13[/tex]
[tex]\angle MKL = 41[/tex]
Solving (a): NK
MK is a diagonal and NK is half of the diagonal. So:
[tex]NK = \frac{1}{2} * MK[/tex]
[tex]NK = \frac{1}{2} * 30[/tex]
[tex]NK = 15[/tex]
Solving (b): JL
JL is a diagonal, and it is twice of NL.
[tex]JL = 2 * NL[/tex]
[tex]JL = 2 * 13[/tex]
[tex]JL = 26[/tex]
Solving (c): KL
To solve for KL, we consider triangle KNL where:
[tex]\angle KNL = 90[/tex]
and
[tex]KL^2 = NL^2 + NK^2[/tex]
[tex]KL^2 = 13^2 + 15^2[/tex]
[tex]KL^2 = 394[/tex]
[tex]KL = \sqrt{394[/tex]
[tex]KL = 19.85[/tex]
Solving (d - h):
To do this, we consider triangle JKN
[tex]\angle KNL = \angle LNM = \angle MNJ = \angle JNK = 90[/tex] -- diagonals bisect one another at right angle
Alternate interior angles are equal. So:
[tex]\angle MKL = \angle KMJ = \angle KJL = \angle JLM = 41[/tex]
Similarly:
[tex]\angle MKJ = \angle KML = \angle MJL = \angle JLK = 90 - 41[/tex]
[tex]\angle MKJ = \angle KML = \angle MJL = \angle JLK = 49[/tex]
So:
[tex]\angle JKM =49[/tex]
[tex]\angle JML =41[/tex]
[tex]\angle MLK = \angle MLJ + \angle JLK[/tex]
[tex]\angle MLK = 49 + 41[/tex]
[tex]\angle MLK = 90[/tex]
[tex]\angle MNL =90[/tex]
[tex]\angle KJL =41[/tex]